Use 'eastward' to specify travel or movement in an eastern direction, rather than a point in space. The birds are flying eastward for the winter.
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Metaphorical Use
'Eastward' can signify progress or new beginnings, referencing the sunrise. The team's success felt like a new eastward horizon.
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Not Eastbound
Don't confuse 'eastward' with 'eastbound', which is often used for transport routes or roads. The plane is heading eastward, but 'Eastbound Flight 77' is its specific route.